Learning multi-view data is an emerging problem in machine learning research, and nonnegative matrix factorization (NMF) is a popular dimensionality-reduction method for integrating information from multiple views. These views often provide not only consensus but also complementary information. However, most multi-view NMF algorithms assign equal weight to each view or tune the weight via line search empirically, which can be infeasible without any prior knowledge of the views or computationally expensive. In this paper, we propose a weighted multi-view NMF (WM-NMF) algorithm. In particular, we aim to address the critical technical gap, which is to learn both view-specific weight and observation-specific reconstruction weight to quantify each view's information content. The introduced weighting scheme can alleviate unnecessary views' adverse effects and enlarge the positive effects of the important views by assigning smaller and larger weights, respectively. Experimental results confirm the effectiveness and advantages of the proposed algorithm in terms of achieving better clustering performance and dealing with the noisy data compared to the existing algorithms.

翻译：学习多视角数据是机器学习研究中的一个新兴问题，非负矩阵分解（NMF）是一种整合多视角信息的常用降维方法。这些视角不仅提供共识信息，还提供互补信息。然而，大多数多视角NMF算法为每个视角分配相等权重，或通过线性搜索凭经验调整权重，这在缺乏视角先验知识时可能不可行，或计算成本高昂。本文提出一种加权多视角NMF（WM-NMF）算法，旨在解决关键的技术空白，即同时学习视角特定权重和观测特定重构权重，以量化每个视角的信息含量。所引入的加权方案通过为不重要视角分配较小权重、为重要视角分配较大权重，可减轻不必要视角的负面影响，并增强重要视角的正面效果。实验结果表明，与现有算法相比，所提算法在实现更优聚类性能和应对噪声数据方面具有有效性和优势。